4. A manufacturer believes that the proportion of shipments of parts that arrive late is p = 0.6. If a random sample of 12 orders shows that four or fewer arrived late, the hypothesis that p = 0.6 will be rejected in favor of the alternative p<0.6. Use the binomial distribution to answer the following. (a) Find the probability of committing a type I error if the true proportion is 0.6. (b) Find the probability of committing a type II error for the specific alternatives p = 0.3 and p = 0.5.